A391152 a(0) = 1; a(n) = n * Sum_{k=1..n} binomial(n,k-1) * a(n-k).

1, 1, 6, 36, 280, 2675, 30216, 394233, 5835464, 96627618, 1769893080, 35531597959, 775839946464, 18306267751369, 464174851794094, 12587054526203820, 363493104803017184, 11137369421602789775, 360867894650798911704, 12328474541846207359441, 442905401932918535022500

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Formula

G.f. A(x) satisfies: A(x) = 1 + x * d/dx ( x * A(x/(1 - x)) / (1 - x)^2 ).

Mathematica

a[0] = 1; a[n_] := a[n] = n Sum[Binomial[n, k - 1] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 20}]
nmax = 20; A[_] = 0; Do[A[x_] = 1 + x D[x A[x/(1 - x)]/(1 - x)^2, x] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Crossrefs

Cf. A006153, A040027, A367308.

Sequence in context: A204210 A366436 A318564 * A259818 A330449 A346547

Adjacent sequences: A391149 A391150 A391151 * A391153 A391154 A391155

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 05 2026

Status

approved